Abstract
The geometric design and shape optimization of complex surfaces are pivotal and knotty techniques in computer aided geometric design (CAGD), and widely used in many complex product manufacturing fields involving surfaces modeling, e.g., for ships, aircraft wing, automobiles, etc. In this paper, an enhanced golden jackal optimization (GJO) algorithm is used to optimize the shape of complex composite shape-adjustable generalized cubic Ball (CSGC-Ball, for short) surfaces. Firstly, the shape design of CSGC-Ball surfaces is mathematically an optimization problem that can be efficiently dealt with by meta-heuristic algorithms. In this regard, an enhanced GJO (EGJO), combined with opposition-based learning, spring vibration-based adaptive mutation and binomial-based cross-evolution strategy, is developed to improve the convergence speed and calculation accuracy of the original GJO. The performance of EGJO is assessed on 23 benchmark test functions, IEEE CEC-2019 and 4 actual engineering optimization problems, and the competition and practicability of EGJO algorithm are confirmed. Secondly, the CSGC-Ball surfaces with global and local shape parameters is constructed based on a class of cubic generalized Ball basis functions, and then the conditions of G1 and G2 continuity for the surfaces are derived. The shapes of CSGC-Ball surfaces can be adjusted and optimized expediently by utilizing their shape parameters. Finally, the minimum energy-based shape optimization models of CSGC-Ball surfaces with 1th-order and 2th-order geometric continuity are established, respectively. Furthermore, the proposed EGJO is utilized to solve the established optimization models, and the CSGC-Ball surfaces with minimum energy are obtained. Four representative examples are given to demonstrate the excellence and effectiveness of EGJO in solving the shape optimization problems of complex CSGC-Ball surfaces.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Data availability
All data generated or analysed during this study are included in this published article.
Code availability
The Matlab source code of the EGJO related to this article can be found online at https://www.researchgate.net/publication/371902375_EGJO_Code.
References
Agushaka O, Ezugwu A, Abualigah L (2022) Dwarf Mongoose optimization algorithm. Comput Methods Appl Mech Eng 391:114570
Arini FY, Sunat K, Soomlek C (2022) Golden Jackal Optimization with joint opposite selection: an enhanced nature-inspired optimization algorithm for solving optimization problems. IEEE Access 10:128800–128823
Ball AA (1974) CONSURF. Part 1: introduction of the conic lofting tile. Comput Aided Des 6(4):243–249
Ball AA (1975) CONSURF. Part 2: description of the algorithms. Comput Aided Des 7:237–242
Ball AA (1977) CONSURF. Part 3: how the program is used. Comput Aided Des 9(1):9–12
Barnhill RE, Riesenfeld RF (1974) Computer aided geometric design. Academic Press, New York
Braik M (2021) Chameleon Swarm Algorithm: a bio-inspired optimizer for solving engineering design problems. Expert Syst Appl 174:114685
Camp CV, Farshchin M (2014) Design of space trusses using modified teaching-learning based optimization. Eng Struct 1:020
Chopra N, Ansari MM (2022) Golden jackal optimization: a novel nature-inspired optimizer for engineering applications. Expert Syst Appl 7:198
Dehghani M, Hubálovský Š, Trojovský P (2022) Tasmanian Devil Optimization: a new bio-inspired optimization algorithm for solving optimization algorithm. IEEE Access 10:19599–19620
Derrac J, García S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evolut Comput 1(1):3–18
Ding DY, Li M (2000) Properties and applications of generalized Ball curve. J Appl Math 23:123–131
Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28–39
Essam HH, Doaa AA, Marwa ME, Mohamed AH, Mina Y (2022) An efficient image segmentation method for skin cancer imaging using improved golden jackal optimization algorithm. Comput Biol Med 149:106075
Faramarzi A, Heidarinejad M, Stephens B, Mirjalili S (2020) Equilibrium optimizer: a novel optimization algorithm. Knowl-Based Syst 191:105190
Gaurav D, Vijay K (2019) Seagull optimization algorithm: theory and its applications for large-scale industrial engineering problems. Knowl-Based Syst 165:169–196
Gellatly RA, Berke L, Gibson W (1971) The use of optimality cretria in automated structural design. In: AFFDL. In: Proceedings of 3rd conference on matrix methods in structural analysis
Gurunathan B, Dhande S (1987) Algorithms for development of certain classes of ruled surfaces. Comput Graph 11(2):105–112
Hashim FA, Hussain K, Houssein EH, Mai SM, Al-Atabany W (2020) Archimedes optimization algorithm: a new metaheuristic algorithm for solving optimization problems. Appl Intell 51:1531–1551
Hayyolalam V, Kazem AAP (2020) Black Widow Optimization Algorithm: a novel meta-heuristic approach for solving engineering optimization problems. Eng Appl Artif Intell 87:203249
Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen HL (2019) Harris hawks optimization: algorithm and applications. Futur Gener Comput Syst 97:849–872
Hu SM, Wang GZ, Jin TG (1996) Properties of two types of generalized Ball curves. Comput Aided Des 28(2):125–133
Hu SM, Wang GJ, Sun JG (1998) A type of triangular Ball surface and its properties. J Comput Sci Technol 13:63–72
Hu GS, Wang D, Yu AM (2009) Construction and application of 2m+2 degree Ball curve with shape parameters. J Eng Graphics 30(5):69–79
Hu G, Luo L, Li R, Yang C (2017) Quartic generalized Ball surfaces with shape parameters and its continuity conditions. In: 2017 6th International Conference on Computer Science and Network Technology (ICCSNT), pp 5–10
Hu G, Wu JL, Li HN, Hu XZ (2020) Shape optimization of generalized developable H-Bézier surfaces using adaptive cuckoo search algorithm. Adv Eng Softw 149:102889
Hu G, Zhu XN, Wei G, Chang CT (2021) An improved marine predators algorithm for shape optimization of developable Ball surfaces. Eng Appl Artif Intell 105:104417
Hu G, Dou WT, Wang XF, Abbas M (2022a) An enhanced chimp optimization algorithm for optimal degree reduction of Said-Ball curves. Math Comput Simul 197:207–252
Hu G, Li M, Wang X, Wei G, Chang CT (2022b) An enhanced manta ray foraging optimization algorithm for shape optimization of complex CCG-Ball curves. Knowl-Based Syst 240:108071
Hu G, Li M, Zhong JY (2022c) Combined cubic generalized ball surfaces: Construction and shape optimization using an enhanced JS algorithm. Adv Eng Soft 103404
Hu G, Du B, Wang XF, Wei G (2022d) An enhanced black widow optimization algorithm for feature selection. Knowl-Based Syst 35:107638
Hu G, Chen LX, Wang XP et al (2022e) Differential evolution-boosted sine cosine golden eagle optimizer with Lévy flight. J Bionic Eng 19:1850–1885
Hu G, Zhong JY, Du B, Guo W (2022f) An enhanced hybrid arithmetic optimization algorithm for engineering applications. Comput Methods Appl Mech Eng 394:114901
Hu G, Yang R, Qin XQ, Wei G (2022g) MCSA: multi-strategy boosted chameleon-inspired optimization algorithm for engineering applications. Comput Methods Appl Mech Eng 403:115676
Hu G, Wang J, Li Y et al (2023a) An enhanced hybrid seagull optimization algorithm with its application in engineering optimization. Eng Comput 38:2821–2857
Hu G, Du B, Wang X (2023b) An improved black widow optimization algorithm for surfaces conversion. Appl Intell 53:6629–6670
Hu G, Zhong J, Wei G, Chang C-T (2023c) DTCSMO: an efficient hybrid starling murmuration optimizer for engineering applications. Comput Methods Appl Mech Eng 405:115878
Hu G, Wang J, Li M, Hussien AG, Abbas M (2023d) EJS: Multi-strategy enhanced jellyfish search algorithm for engineering applications. Mathematics 11(4):851
Jafari M, Salajegheh E, Salajegheh J (2021) Elephant clan optimization: a nature-inspired metaheuristic algorithm for the optimal design of structures. Appl Soft Comput 113:107892
Jaklič G, Žagar E (2011) Curvature variation minimizing cubic Hermite interpolants. Appl Math Comput 218(7):3918–3924
Jiang P, Wu H (2004) Dual basis of Wang-Ball basis functnd its application. J Comput Aided Des Graph 16(4):454–458
Kaur S, Awasthi LK, Sangal AL et al (2020) Tunicate Swarm Algorithm: a new bio-inspired based metaheuristic paradigm for global optimization. Eng Appl Artif Intell 90:103541
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Network, Perth, Australia, pp 1942–1948
Kumar SN, Nalin KM (2022) Modified Golden Jackal Optimization assisted adaptive fuzzy PIDF controller for virtual inertia control of micro grid with renewable energy. Symmetry 14:1946
Li WZ, Wang L, Cai XJ, Hu JJ, Guo WA (2019) Species co-evolutionary algorithm: a novel evolutionary algorithm based on the ecology and environments for optimization. Neural Comput Appl 31(7):2015–2024
Liang S, Fang AY, Sun G, Qu GN (2022) Biogeography-based optimization with adaptive migration and adaptive mutation with its application in sidelobe reduction of antenna arrays. Appl Soft Comput 121:108772
Lichuan H, Mingyu D, Jiuyang W (2022) Magnetic levitation system control and multi-objective optimization using Golden Jackal Optimization. In: 2022 2nd International Conference on Electrical Engineering and Mechatronics Technology, Hangzhou, China, pp 193–197
Liu C, Li J (2016) Study on the optimal shape parameter of parametric curves based on PSO algorithm. J Interdiscip Math 19(2):321–333
Liu HY, Li L, Zhang DM (2011) Quadratic Ball curve with shape parameters. J Shandong Univ 41(2):23–28
Lu LZ (2015) A note on curvature variation minimizing cubic Hermite interpolants. Appl Math Comput 259:596–599
Mehrdad P, Keyvan A, Armin S et al (2022) Model parameters estimation of the proton exchange membrane fuel cell by a Modified Golden Jackal Optimization. Sustain Energy Technol Assess 53:102657
Mhmed M, Hasanien HM, Turky RA (2023) Modeling and optimal operation of hybrid wave energy and PV system feeding supercharging stations based on golden jackal optimal control strategy. Energy 263:125932
Mirjalili S (2016) SCA: A sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133
Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey Wolf optimizer. Adv Eng Softw 69:46–61
Najjar I, Sadoun A, Fathy A, Abdallah A (2022) Prediction of tribological properties of alumina-coated, silver-reinforced copper nanocomposites using long short-term model combined with Golden Jackal Optimization. Lubricants 10:277
Naruei I, Keynia F (2021) A new optimization method based on COOT bird natural life model. Expert Syst Appl 183:115352
Othlnan W, Goldman RN (1997) The dual basis functions for the generalized ball basis of odd degree. Comput Aided Geom Des 14(6):571–582
Pelusi D, Mascella R, Tallini L et al (2019) An improved Moth-Flame optimization algorithm with hybrid search phase. Knowl-Based Syst 191:105277
Rao RV, Savsani VJ, Vakharia D (2012) Teaching-learning-based optimization: an optimization method for continuous non-linear large scale problems. Inf Sci 183:1–15
Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179:2232–2248
Said HB (1989) A generalized ball curve and its recursive algorithm. ACM Trans Graph 8(4):360–371
Seyyedabbasi A, Kiani F (2022) Sand Cat swarm optimization: a nature-inspired algorithm to solve global optimization problems. Eng Comput. https://doi.org/10.1007/s00366-022-01604-x
Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous Spaces. J Glob Optim 11:341–359
Tijani S, Mu’Azu MB, Shaaban Y, Adedokun E (2021) A novel Smell Agent Optimization (SAO): an extensive CEC study and engineering application. Knowl-Based Syst 232:107486
Tizhoosh HR (2005) Opposition-based learning: a new scheme for machine intelligence. IEEE 1:695–701
Trojovský P, Dehghani M (2022) Pelican optimization algorithm: a novel nature-inspired algorithm for engineering applications. Sensors 22(3):855
Van Laarhoven PJ, Aarts EH (1987) Simulated annealing. In: Simulated annealing. Theory and applications, pp 7–15
Wang GJ (1987) High order Ball curve and its geometric properties. J Appl Math Coll Univ A 1:126–140
Wang CW (2008) Extension of cubic Ball curve. J Eng Graph 29(1):77–81
Wang CW (2009) The extension of the quartic Wang-Ball curve. J Eng Graph 30(1):80–84
Wang GJ, Jiang SR (2004) The algorithms for evaluating two new types of generalized Ball curves/surfaces and their applications. Acta Math Appl Sin 4(1):52–63
Wang GJ, Liu LG (2015) Approximation and processing of geometric calculation. Science Press, Beijing
Wang LY, Cao QJ, Zhang ZX (2022) Artificial rabbits optimization: a new bio-inspired meta-heuristic algorithm for solving engineering optimization problems. Eng Appl Artif Intell 114:105082
Wang Z, Mo Y, Cui M, Hu J, Lyu Y (2023) An improved golden jackal optimization for multilevel thresholding image segmentation. PLoS ONE 18(5):e0285211
Wilcoxon F, Bulletin SB, Dec N (1992) Individual comparisons by ranking methods. Springer, New York
Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1:67–82
Wu HY (2000) Two new kinds of generalized Ball curves. J Appl Math 23(02):196–205
Xi MC (1997) Dual basis of Ball basis function and its application. Comput Math 2147–153
Xiong J, Guo QW (2012) Generalized Said-Ball curves. J Numer Methods Comput Appl 33(1):32–40
Xiong J, Guo QW (2013) Generalized Wang-Ball curves. J Numer Methods Comput Appl 34(3):187–195
Yan LL, Zhang W, Wen RS (2011) Two types of shape-adjustable fifth-order generalized Ball curves. J Eng Grap 32(6):16–20
Yang J, Xiong J, Chen YL, Yee PL, Ku CS, Babanezhad M (2023) Improved Golden Jackal optimization for optimal allocation and scheduling of wind turbine and electric vehicles parking lots in electrical distribution network using Rosenbrock’s direct rotation strategy. Mathematics 11(6):1415
Yuan PL, Zhang TH, Yao LG, Lu Y, Zhuang WB (2022a) A Hybrid Golden Jackal Optimization and Golden Sine Algorithm with dynamic lens-imaging learning for global optimization problems. Appl Sci 12:9709
Yuan YL, Ren JJ, Wang S, Wang ZX, Mu XK, Zhao W (2022b) Alpine skiing optimization: a new bio-inspired optimization algorithm. Adv Eng Softw 170:103158
Acknowledgements
This work is supported by the National Natural Science Foundation of China (Grant No. 51875454).
Author information
Authors and Affiliations
Contributions
GH, LC and GW wrote the main manuscript text and LC prepared all figures. All authors reviewed the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Hu, G., Chen, L. & Wei, G. Enhanced golden jackal optimizer-based shape optimization of complex CSGC-Ball surfaces. Artif Intell Rev 56 (Suppl 2), 2407–2475 (2023). https://doi.org/10.1007/s10462-023-10581-6
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10462-023-10581-6